A simplified account of the correlation effects to bond breaking processes: The Brillouin-Wigner perturbation theory using a multireference formulation

Abstract

Adaptation of improved virtual orbital complete active space configuration interaction functions in state-specific multireference perturbation theory motivated by the Brillouin-Wigner perturbation scheme using Møller-Plesset multipartitioning is examined. The method, denoted as IVO-BWMRPT, focuses on only the root of principal interest at a time using single-root parameterization of Jeziorski-Monkhorst ansatz within the frame of an effective Hamiltonian. This approach yields size-extensive energy and avoids intruder-state problems in a natural manner. It allows relaxation of the reference space wave function in the presence of the perturbation which produces an important differential effect on the energy and cannot be neglected for quasidegenerate electronic states. The method has been tested against nontrivial situations such as the Be + H2 insertion profile along with the energy surfaces of FH and X2 (X = F, Cl, and Br), in which conventional single-reference methods generally fail, exhibiting very encouraging findings. We also consider the energy surfaces of ethylene (by breaking the π bond as well as the CC bond) and for the twisting of tetramethyleneethane. IVO-BWMRPT represents a rather balanced protocol for the description of molecules at a wide range of geometries, including stretched or dissociating bonds. Close agreement of our estimates with the reference values provides a useful measure for the success of the IVO-BWMRPT method to treat strongly correlated systems. Our results for TME show that the singlet state always lies below the triplet state for different conformations. The IVO-BWMRPT furnishes a compact and correct representation of the MR-wave function, and hence, a large variety of quasidegenerate situations can be accommodated within the method.

Investigation of Multiple-Bond Dissociation Using Brillouin–Wigner Perturbation with Improved Virtual Orbitals

“…A brief description and the basic underlying idea of the IVO-BWMRPT method, where only one root is supposed to be exact in the limit (the target electronic state), is discussed here in order to introduce the necessary notation and terminology as the details of the method have been described in ref 55. The origin of the parent method has been described in detail in refs 18 and 25. The main essence of the SSMR scheme is to reduce a multistate MR problem to a single state MR one, so that the resulting working equations can provide information about the state of interest.…”

“…In the IVO-BWMRPT method, the description of the target state obtained by the IVO-CASCI scheme can be systematically improved by employing second-order perturba-tive treatment of electron correlation using the SS MRPT approach within the BW framework. 55 In practice, the perturbative corrections to the MR mean-field reference play an important role in getting a quantitative accuracy. Although most MRPTs are beset by numerical divergence due to the intruder states problem (spoil computations with unphysical contributions problematic to heal systematically), 56−61 the IVO-BWMRPT methodology circumvents this obstacle in a natural and size-extensive manner because the IVO modification of the state-specific BWMRPT scheme retains all the advantages of the parent SSMR protocol of Mukherjee et al 18,52 that make it a serious candidate for efficient description of the dissociation of molecular bonds correctly and to compute global energy surfaces.…”

“…The usefulness of the MRPT method (based on the distinction between nondynamical (or static) and dynamical correlation effects) can be extended using the improved virtual orbital (IVOs) complete active space configuration interaction (CASCI) technique (IVO-CASCI) , to generate a reference function. Our recently suggested state-specific (SS) Brillouin–Wigner MRPT (BWMRPT) with IVOs [termed IVO-BWMRPT], treating all components of the model space on the same footing, offers a useful and efficient ab initio protocol for studying near-degenerate states at an affordable computational cost. Contrary to the multistate strategies, SS schemes focus on only one electronic state at a time.…”

“…It builds an effective Hamiltonian matrix in the reference space under the impact of perturbation at the level of second order, and its diagonalization supplies the mixing of the perturbed states and energy of the state under consideration. In the IVO-BWMRPT method, the description of the target state obtained by the IVO-CASCI scheme can be systematically improved by employing second-order perturbative treatment of electron correlation using the SS MRPT approach within the BW framework . In practice, the perturbative corrections to the MR mean-field reference play an important role in getting a quantitative accuracy.…”

Single-Root Multireference Brillouin–Wigner Perturbative Approach to Excitation Energies

“… 65 The resulting method, IVO-CASCI, 65 , 66 is cost-effective since it does not require additional costly iterations beyond an initial SCF calculation. Recently, a new version of the SSMRPT method with the IVO-CASCI reference function within the framework of Brillouin–Wigner (BW) perturbation (called IVO-BWMRPT) 50 has been developed by our group. The IVO-BWMRPT is endowed with all of the redeeming formal properties of the parent method.…”